非椭圆非线性Schr(o|¨)dinger方程H^s整体解

Global H^S-Solutions of Generalized Nonlinear Schr(o|¨)dinger Equations

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摘要对含L2次临界指数非线性项的非椭圆型Schrodinger方程柯西问题进行了讨论,用Strichartz不等式和压缩映像原理证明了方程有HS局部解,由L2守恒律得到方程的HS整体解． In the present paper, the nonlinear nonelliptic Schrbdinger equation with L^2 subcritical power is studied. With the aid of Strichartz＇ inequality, the author proves the existence of global H^s-solutions u（t） of nonelliptic NLS equation and u（t） ∈ C （R, H^s（R^n）） if the initial date ψ0 ∈ H^s （R^n）, 0 ≤ s ≤ 1.

作者朱继德

机构地区解放军理工大学理学院

出处《数学年刊（A辑）》 CSCD 北大核心 2006年第4期477-490,共14页 Chinese Annals of Mathematics

关键词非椭圆型Schroedinger方程柯西问题 BESOV空间整体解 Nonelliptic NLS equation, Cauchy problem, Besov space,Global solution

分类号 O175.29 [理学—基础数学]

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参考文献16

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二级参考文献1

1Wang Baoxiang Department of Mathematics. Hebei University, Baoding 071002, China.Bessel (Riesz) Potentials on Banach Function Spaces and Their Applications I Theory[J].Acta Mathematica Sinica,English Series,1998,14(3):327-340. 被引量：4

共引文献3

1朱继德.非线性双曲型Schrdinger方程L^2整体解的存在性[J].数学年刊（A辑）,2005,26(4):495-506.
2沈彩霞.一类广义Davey-Stewartson方程关于初值问题的解[J].河北大学学报（自然科学版）,2002,22(1):75-76.
3曹晓东,郭留涛.一类非椭圆薛定谔方程的Cauchy问题的光滑性效应[J].数学杂志,2022,42(6):523-532.

1许宁.5维半线性色散方程弱解的正则性[J].常熟理工学院学报,2009,23(8):1-10.
2朱继德.非线性双曲型Schrdinger方程L^2整体解的存在性[J].数学年刊（A辑）,2005,26(4):495-506.
3叶耀军,王建平.一类非线性Schrdinger方程的整体解和自相似解[J].系统科学与数学,2008,28(6):751-757.

数学年刊（A辑）

2006年第4期

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非椭圆非线性Schr(o|¨)dinger方程H^s整体解

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